The home side had far more chances than the team from Azerbaijan in the first half but fell behind in the 40th minute when Spanish midfielder Michel rose to meet a corner and delivered too powerful a header for Jan Oblak to keep out.
Midfielder Thomas Partey equalised in the 56th minute with a thunderous long-range strike and Atletico were given another boost when Brazilian Pedro Henrique was sent off a minute later.
Yet despite laying siege to the visitors' area, Atletico could not find a winner and, to complete their miserable night, they also had their own defender Stefan Savic sent off for a second booking in the 88th minute.
"We always tried to win the game but sometimes in this beautiful sport things don't go your way and the ball just didn't want to go in," said Atletico coach Diego Simeone.
"We have to keep on fighting in the same way, the work of the players is spectacular, we have to keep believing in this team, and I do."
Atletico, Champions League runners up in 2014 and 2016 and semi-finalists last season, are third in Group C on three points, five behind leaders AS Roma and four behind Chelsea.
It means Atletico now need to hope for something remarkable to avoid a group stage exit for the first time since returning to Europe's elite competition in 2013.
Even if they beat Roma and Chelsea in their final two games, they will still need either the Italian side or Premier League champions to drop points against Qarabag.
Should they draw with Roma in their next outing, they will need Chelsea to lose to Qarabag to have any chance of moving forward.
Atletico went into the must-win game on the back of a disappointing 1-1 draw with Villarreal at home on Saturday and with only one win in their previous seven games in all competitions.
They made a bright start as Antoine Griezmann hooked a venomous volley from outside the box to force a fine save from Ibrahim Sehic.
The sight of the Bosnian goalkeeper repelling shots from the hosts became a familiar sight for the angst-ridden home fans in the Wanda Metropolitano stadium, which has yet to witness an Atletico win in the Champions League.
After Partey's sensational equaliser, Simeone continued his familiar routine at home games of waving his arms around to encourage the supporters to will on his side, but every time they came forward Sehic got in their way.
He thwarted Kevin Gameiro, Diego Godin and captain Gabi in the second half before the final whistle sounded, signalling a likely end to Atletico's recent thrilling spell in Europe's top competition.
(Reporting by Richard Martin; Editing by Toby Davis and Ian Chadband)
Share
